The present invention relates to a method, a device, and a corresponding computer program product for calculating (optimizing) and producing a spectacle lens taking into consideration higher-order aberrations of both the eye and the spectacle lens.
For the production or optimization of spectacle lenses, in particular of individual spectacle lenses, each spectacle lens is manufactured such that the best possible correction of a refractive error of the respective eye of the spectacles wearer is obtained for each desired direction of sight or each desired object point. In general, a spectacle lens is said to be fully corrective for a given direction of sight if the values sphere, cylinder, and axis of the wavefront upon passing the vertex sphere match with the values for sphere, cylinder, and axis of the prescription for the eye having the visual defect. In the refraction determination for an eye of a spectacles wearer, dioptric values (particularly sphere, cylinder, cylinder axis) for a far (usually infinite) distance and optionally (for multifocal or progressive lenses) an addition for a near distance (e.g. according to DIN 58208) are determined. In this way, the prescription (in particular sphere, cylinder, cylinder axis, and optionally addition) that is sent to a spectacles manufacturer is stipulated. In modern spectacle lenses, object distances deviating from the standard, which are used in the refraction determination, can be indicated additionally.
However, a full correction for all directions of sight at the same time is normally not possible. Therefore, the spectacle lenses are manufactured such that they achieve a good correction of visual defects of the eye and only small aberrations in the main regions of use, especially in central visual regions, while larger aberrations are permitted in peripheral regions.
In order to be able to manufacture a spectacle lens in this way, the spectacle lens surfaces or at least one of the spectacle lens surfaces is first of all calculated such that the desired distribution of the unavoidable aberrations is effected thereby. This calculation and optimization is usually performed by means of an iterative variation method by minimization of a target function. As a target function, particularly a function F having the following functional connection with the spherical power S, the magnitude of the cylindrical power Z, and the axis of the cylinder a (also referred to as “SZA” combination) is taken into account and minimized:
  F  =            ∑              i        =        1            m        ⁢                  ⁢                  [                                                            g                                  i                  ,                                      S                    ⁢                                                                                  ⁢                    Δ                                                              ⁡                              (                                                      S                                          Δ                      ,                      i                                                        -                                      S                                          Δ                      ,                      i                      ,                      target                                                                      )                                      2                    +                                                    g                                  i                  ,                                      Z                    ⁢                                                                                  ⁢                    Δ                                                              ⁡                              (                                                      Z                                          Δ                      ,                      i                                                        -                                      Z                                          Δ                      ,                      i                      ,                      target                                                                      )                                      2                    +          …                ⁢                                  ]            .      
In the target function F, at the evaluation points i of the spectacle lens, at least the actual refractive deficits of the spherical power SΔ,i and the cylindrical power ZΔ,i as well as target values for the refractive deficits of the spherical power SΔ,i,target and the cylindrical power ZΔ,i,target are taken into consideration.
It was found in DE 103 13 275 that it is advantageous to not indicate the target values as absolute values of the properties to be optimized, but as their deviation from the prescription, i.e. as the required misadjustment. This has the advantage that the target values are independent of the prescription (SphV,ZylV,AxisV,PrV,BV) and that the target values do not have to be changed for every individual prescription. Thus, as “actual” values of the properties to be optimized, not absolute values of these optical properties are taken into account in the target function, but the deviations from the prescription. This has the advantage that the target values can be specified independent of the prescription and do not have to be changed for every individual prescription.
The respective refractive deficits at the respective evaluation points are preferably taken into consideration with weighting factors gi,SΔ and gi,ZΔ. Here, the target values for the refractive deficit of the spherical power SΔ,i,target and/or the cylindrical power ZΔ,i,target, particularly together with the weighting factor gi,SΔ and gi,ZΔ, form the so-called spectacle lens design. In addition, particularly further residues, especially further parameters to be optimized, such as coma and/or spherical aberration and/or prism and/or magnification and/or anamorphic distortion, etc., can be taken into consideration, which is particularly implied by the expression “+ . . . ”.
In some cases, this can contribute to a clear improvement particularly of an individual adjustment of a spectacle lens if in the optimization of the spectacle lens not only aberrations up to the second order (sphere, magnitude of astigmatism, and cylinder axis), but also higher-order aberrations (e.g. coma, trefoil, spherical aberration) are taken into consideration.
It is known from the prior art to determine the shape of a wavefront for optical elements and particularly spectacle lenses that are delimited by at least two refractive boundary surfaces. For example, this can be done by means of a numerical calculation of a sufficient number of neighboring rays, along with a subsequent fit of the wavefront data by Zernike polynomials. Another approach is based on local wavefront tracing in the refraction (cf. WO 2008/089999 A1). Here, only one single ray (the main ray) per visual point is calculated, accompanied by the derivatives of the vertex depth of the wavefront according to the transversal coordinates (perpendicular to the main ray). These derivatives can be formed up to a specific order, wherein the second derivatives describe the local curvature properties of the wavefront (such as refractive power, astigmatism) and the higher derivatives are connected with the higher-order aberrations.
In the tracing of light through a spectacle lens, the local derivatives of the wavefront are calculated at a suitable position in the course of the ray in order to compare them with desired values obtained from the refraction of the spectacle lens wearer. This position can be the vertex sphere, for example. In this respect, it is assumed that a spherical wavefront starts at the object point and propagates up to the first spectacle lens surface. There, the wavefront is refracted and subsequently propagates to the second spectacle lens surface, where it is refracted again. If further surfaces exist, the alternation of propagation and refraction will be continued until the last boundary surface has been passed. The last propagation takes place from this last boundary surface to the vertex sphere.
WO 2008/089999 A1 discloses the laws of refraction at refractive surfaces not only for aberrations or optical properties of second order, but also for higher orders. If a wavefront with local derivatives known up to a specific order is obliquely incident on a boundary surface, the vertex depth of which can itself be described by known local derivatives up to the same order, then the local derivatives of the outgoing wavefront can be calculated up to the same order with the calculation methods according to WO 2008/089999 A1. Such a calculation, particularly up to the second order, is very helpful for assessing the image formation properties or optical properties of a spectacle lens in the wearing position. Specifically, such a calculation is of great importance if a spectacle lens is to be optimized in the wearing position over all visual points.
Even if the process of refraction can be described and calculated very efficiently therewith, the consideration of higher-order aberrations remains very expensive nevertheless, since especially the required iterative ray tracing for the propagation of the wavefronts involves great computing effort.